Proof No. 2 Andrew Jones Taken from

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Presentation transcript:

Proof No. 2 Andrew Jones Taken from www.cut-the-knot.org Pythagorean Theorem Proof No. 2 Andrew Jones Taken from www.cut-the-knot.org

We start with two squares with sides a and b, respectively, placed side by side. The total area of the two squares is a2+b2.

The construction did not start with a triangle but now we draw two of them, both with sides a and b and hypotenuse c. Note that the segment common to the two squares has been removed. At this point we therefore have two triangles and a strange looking shape.

As a last step, we rotate the triangles 90˚, each around its top vertex. The right one is rotated clockwise whereas the left triangle is rotated counterclockwise. Obviously the resulting shape is a square with the side c and area c2.

So when you put it all together A2 + B2 = C2.